I tried many times and once lost to the last boss after defeating 8 bosses in 112 turns. I then removed the Sharpen Emerald Saber on Vesper and retreated once, but finished defeating 8 of them in 119 turns and was able to complete the game in a total of 177 turns.
The Arcade mode has a seemingly strict turn limit, but it was a very fun mode to figure out the strategy. MEOOOOOOW!!!